2010/04/12 by Tianxiao Wang, Wang, Tianxiao, Yufeng Shi +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H07 #60H20 #91B30 #93E20 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #msc:60H07 #msc:60H20 #msc:91B30 #msc:93E20 #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1004.2206
28 pages
arxiv created 2010/04/12 · openalex publication_date 2010/04/12 · arxiv updated 2010/04/14 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present to illustrate the aforementioned optimal control problem. Motivated by the technical skills in solving above problem, a more convenient and briefer method for the unique solvability of M-solution for BSVIEs is proposed. At last, we will investigate a risk minimization problem by means of the maximum principle for FBSVIEs. Closed-form optimal portfolio is obtained in some special cases.